A Robust Grid-Based Meshing Algorithm for Embedding Self-Intersecting Surfaces
Abstract
The creation of a volumetric mesh representing the interior of an input polygonal mesh is a common requirement in graphics and computational mechanics applications. Most mesh creation techniques assume that the input surface is not self-intersecting. However, due to numerical and/or user error, input surfaces are commonly self-intersecting to some degree. The removal of self-intersection is a burdensome task that complicates workflow and generally slows down the process of creating simulation-ready digital assets. We present a method for the creation of a volumetric embedding hexahedron mesh from a self-intersecting input triangle mesh. Our method is designed for efficiency by minimizing use of computationally expensive exact/adaptive precision arithmetic. Although our approach allows for nearly no limit on the degree of self-intersection in the input surface, our focus is on efficiency in the most common case: many minimal self-intersections. The embedding hexahedron mesh is created from a uniform background grid and consists of hexahedron elements that are geometrical copies of grid cells. Multiple copies of a single grid cell are used to resolve regions of self-intersection/overlap. Lastly, we develop a novel topology-aware embedding mesh coarsening technique to allow for user-specified mesh resolution as well as a topology-aware tetrahedralization of the hexahedron mesh.
Cite
@article{arxiv.2201.06256,
title = {A Robust Grid-Based Meshing Algorithm for Embedding Self-Intersecting Surfaces},
author = {Steven W. Gagniere and Yushan Han and Yizhou Chen and David A. B. Hyde and Alan Marquez-Razon and Joseph Teran and Ronald Fedkiw},
journal= {arXiv preprint arXiv:2201.06256},
year = {2024}
}